Linear Operators: Spectral theory |
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Page 875
... isomorphism of X onto all of C ( 4 ) . It will also be shown that this isomorphism is a * -isomorphism , i.e. , one preserving the operation of involution . This basic result , which is due to Gelfand and Naĭmark , will find many ...
... isomorphism of X onto all of C ( 4 ) . It will also be shown that this isomorphism is a * -isomorphism , i.e. , one preserving the operation of involution . This basic result , which is due to Gelfand and Naĭmark , will find many ...
Page 878
... isomorphism of B * ( x ) onto C ( o ( x ) ) that we wish to single out . In the notation of the preceding proof the * -isomorphism y↔y ( x ̄1 ( • ) ) of B * ( x ) onto C ( σ ( x ) ) has the property that a corre- sponds to the function ...
... isomorphism of B * ( x ) onto C ( o ( x ) ) that we wish to single out . In the notation of the preceding proof the * -isomorphism y↔y ( x ̄1 ( • ) ) of B * ( x ) onto C ( σ ( x ) ) has the property that a corre- sponds to the function ...
Page 1373
... isomorphism Ŷ of E ( A ) L¿ ( I ) onto L¿ ( A , { ^ ,, } ) . It follows similarly that this same limit exists in the topology of La ( A , { A1j } ) for each fe L ( 1 ) , and defines an isometric isomorphism of E ( A ) L2 ( I ) onto L2 ...
... isomorphism Ŷ of E ( A ) L¿ ( I ) onto L¿ ( A , { ^ ,, } ) . It follows similarly that this same limit exists in the topology of La ( A , { A1j } ) for each fe L ( 1 ) , and defines an isometric isomorphism of E ( A ) L2 ( I ) onto L2 ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero